United Nations-brokered peace talks on the Yemen crisis continued into a third disagreement-marred day on Wednesday, as fighting continued throughout the country and Saudi-led coalition airstrikes in the south were reported to have killed at least 31 civilians.

The discussions began in Geneva on Monday and include representatives of exiled president Abd Rabbu Mansour Hadi's government, the Houthi rebels, and their allies from former president Ali Abdullah Saleh's General Peoples' Congress. UN officials opened proceedings by appealing for a humanitarian ceasefire and mutual rapprochement, but the Houthis arrived a day late and since then, both they and the government have accused each other of trying to obstruct the process and have made little headway.

The sides remain divided and are understood to remain ensconced in separate rooms as of Wednesday, relying on go-betweens for communication. UN special envoy for Yemen Ismail Ould Cheikh Ahmed acknowledged the process would be difficult, but told reporters that just getting the two sides in Geneva was a "great achievement."

Nevertheless, Ahmed added that they must speak in person in order to reach a resolution. "In a situation like this, the Yemenis need to talk among themselves, not with the United Nations," he said, according to remarks carried by AFP. "As long as we have not reached the point where the Yemenis agree together, this will be very difficult."

The Houthis have also brought a team of 22 rather than a previously agreed upon 10, AFP added, something Ahmed is trying to remedy. A Houthi delegate Ghaleb Mutlak said they were hoping to reach a ceasefire agreement for Ramadan, which begins Wednesday evening, and that it would negotiate for as long as it took to agree a stop to the fighting.

On Tuesday, however, the Houthis blasted Hadi's government for using Ahmed as a "tool" to control the talks to their liking.

"Leave to the United Nations some neutrality to continue its mission," said the group's leader Abdul Malik al-Houthi, according to Al Jazeera. "Stop your continuous attempts to control its new envoy." The Houthis had previously blamed their delay in arriving on the Saudi coalition, which backs Hadi and has launched an ongoing series of airstrikes against them.

The government, meanwhile, is refusing to compromise on its demands for a complete Houthi pullout from the large portion of the country now under rebel control, which includes the capital of Sanaa.

Hadi's government has been based in Riyadh since he fled there in February, but loyalists are battling the Houthis and some allied army remnants who back Saleh. The coalition, which contains a number of other Arab countries, has been bombing the rebels since March. More than 2,500 people have now lost their lives in the fighting.

The death toll continued to climb this week. A civilian convoy was hit by two airstrikes as they attempted to escape fighting in the coastal city of Aden Wednesday, medical sources told the Associated Press, describing charred vehicles and body parts strewn across the road.

Further airstrikes were also reported to have targeted army bases in Sanaa as well as Houthi positions in the central parts of the country and in al-Mahweet province, Reuters said.

Fierce fighting continues elsewhere too. AP cited medical officials and witnesses as saying that more than 30 civilians have been killed by Houthi shelling over the past two days.

Yemen's political transition since Saleh was ousted in 2012's Arab Spring-inspired uprising had been widely seen as a rare success story. But the impoverished state has been increasingly troubled since the Houthis swept down from their northern homelands in September and overran Sanaa. The avowedly anti-America and anti-Israeli rebels are accused of being used by Saleh to restore his power and influence in the country.

The Saudi-led airstrikes have had little success in dislodging the Houthis from captured territory, and have been criticized for the deaths of hundreds of civilians.

The World Health Organization said Friday that as of June 7, 2,584 people had been killed and a further 11,065 wounded in the fighting. About 20 million people, almost 80 percent of the country's population, are now in urgent need of humanitarian assistance, the UN said last week. Fuel, food, and medicine prices have skyrocketed since the fighting began; fuel shortages have closed down many hospitals, and humanitarian agencies are at risk of being unable to operate at all.